Your question is difficult, not knowing the rest of your equipment.
My first thought is to try the Lukaschek PP1 phono stage that was specifically designed to go with your Benz. If that were paired up with the Bryston, you could at least separate ( sonically ) which product was contributing what to the overall sound.
Other phono stages could stand in for the Lukaschek, and any good tube unit should make satisfying mids, with the bass having at bit more of the bloom and output you seem to crave.
Let us know if you make a trial run and what the results were.
My first thought is to try the Lukaschek PP1 phono stage that was specifically designed to go with your Benz. If that were paired up with the Bryston, you could at least separate ( sonically ) which product was contributing what to the overall sound.
Other phono stages could stand in for the Lukaschek, and any good tube unit should make satisfying mids, with the bass having at bit more of the bloom and output you seem to crave.
Let us know if you make a trial run and what the results were.